On (IO,O)-fuzzy rough sets based on overlap functions

Abstract

In the last past years, as a class of continuous binary aggregation functions, there are many scholars keeping a watchful focus on overlap functions for their widely applicability in various actual problems. On the other side, after that rough sets were presented as a formal tool to handle indetermination and inaccuracy in the analysis of data, there arise many works concerning the extension study of rough approximation operators in rough set model. This paper mainly discusses the so-called (IO,O)-fuzzy rough set model obtained through extending the classical conjunction operator in rough approximation operator to overlap functions. Firstly, we investigate a number of essential properties of (IO,O)-fuzzy rough sets, especially for the connections between the obtained new fuzzy rough approximation operators and fuzzy relations. Secondly, we give the topological properties of (IO,O)-fuzzy rough sets. Finally, we show a brief comparison of the (IO,O)-fuzzy rough sets with other common fuzzy rough set models.